Lattice length for Zincblende structures

[nefizseal]

So we have the covalent Radii of Ga = 1.26 A and As = 1.19 A. And the structure is Zinc blende with arsenic occupying half of the tetrahedral sites. So its probably not close packed...

The formula the works for me is, [4/sqrt(3)] x [ radius of Ga + radius of As ]. I can get the answer ( 5.66 A ) by this but I don't know why or how it works? Can someone please explain the reasoning behind it.

Also I noticed this is like the formula for the Body centre cubic packing. Is there any corelation?
thx...

 

[Borek]

Without looking at the structure - such things can be always calculated just by simple geometry. Draw the cell, assume atoms "touch" each other, draw distances between atom centers, use whatever is needed to solve the triangles present.